In a diagram of a bridge, m∠1=87°. If ∠1 and ∠3 are vertical angles, and ∠2 and ∠3 are supplementary, what equation can you write to solve for the value of m∠2? Let m∠2=x .

Answer 1

Since ∠1 and ∠3 are vertical angles, we know that m∠1 = m∠3 = 87°.
Since ∠2 and ∠3 are supplementary, we know that m∠2 + m∠3 = 180°.

From these two equations, we can set up an equation to solve for the value of m∠2, denoted as x:

x + 87° = 180°

Answer 2

If m∠B=58°, and the sum of m∠E and m∠D is 121° , what is the measure of ∠D?

Answer 3

The sum of the angles in a triangle is 180 degrees. Since ∠B and ∠D are angles in the same triangle, we can set up the equation:

m∠B + m∠D + m∠E = 180°

Substituting the given values:

58° + m∠D + m∠E = 180°

We also know that the sum of m∠E and m∠D is 121 degrees:

m∠E + m∠D = 121°

We can substitute this equation into the previous one to solve for the measure of ∠D:

58° + (m∠E + m∠D) = 180°

58° + 121° = 180°

m∠D = 180° - 58° - 121°

m∠D = 1°